if a/b = 1/3, b/c=2, c/d = 1/2, d/e=3, and e/f=1/4 then find the value of abc/def?
A) 3/8
B) 27/8
C) 3/4
D) 27/4
E) 1/4
ans: A
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if a/b = 1/3, b/c=2, c/d = 1/2, d/e=3, and e/f=1/4 then find
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GMATinsight
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Brent@GMATPrepNow
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Assign some values to the given variables.GMATinsight wrote:if a/b = 1/3, b/c=2, c/d = 1/2, d/e = 3, and e/f = 1/4 then find the value of abc/def?
A) 3/8
B) 27/8
C) 3/4
D) 27/4
E) 1/4
ans: A
Given: a/b = 1/3
Let a = 2 and b = 6
Given: b/c = 2
Since b = 6, it must be the case that c = 3
Given: c/d = 1/2
Since c = 3, it must be the case that d = 6
Given: d/e=3
Since d = 6, it must be the case that e = 2
Given: e/f = 1/4
Since e = 2, it must be the case that f = 8
So, abc/def = (2)(6)(3)/(6)(2)(8)
= 36/96
= 3/8
Answer: A
Brent Hanneson - Creator of GMATPrepNow.com
By looking at what is being asked we can see - abc/def = a/d*b/e*c/f
a/d = a/b*b/c*c/d = 1/3*2*1/2 = 1/3
b/e = b/c*c/d*d/e = 2*1/2*3= 3
c/f = c/d*d/e*e/f = 1/2*3*1/4 =3/8
abc/def = 1/3*3*3/8 = 3/8
Answer: A
a/d = a/b*b/c*c/d = 1/3*2*1/2 = 1/3
b/e = b/c*c/d*d/e = 2*1/2*3= 3
c/f = c/d*d/e*e/f = 1/2*3*1/4 =3/8
abc/def = 1/3*3*3/8 = 3/8
Answer: A
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Jay@ManhattanReview
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We haveGMATinsight wrote:if a/b = 1/3, b/c=2, c/d = 1/2, d/e=3, and e/f=1/4 then find the value of abc/def?
A) 3/8
B) 27/8
C) 3/4
D) 27/4
E) 1/4
ans: A
a/b = 1/3 ---(1),
b/c = 2/1 ---(2),
c/d = 1/2 ---(3),
d/e = 3/1 ---(4),
e/f = 1/4 ---(5)
We have to find out the value of abc/def.
abc/def = (a/f)*(b/e)*(c/d)
a/f = (1)*(2)*(3)*(4)*(5) = 1/3 * 2/1 * 1/2 * 3/1 * 1/4 = 1/4;
b/e = (2)*(3)*(4) = 2/1 * 1/2 * 3/1 = 3/1
=> abc/def = (a/f)*(b/e)*(c/d) = 1/4 * 3/1 * 1/2 = [spoiler]3/8[/spoiler].
The correct answer: A
Hope this helps!
Relevant book: Manhattan Review GMAT Math Essentials Guide
-Jay
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Pritish7805
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Let's see how we can modify the expression.
As we have one abc in the denominator and both the terms with b per the given data can be cancelled out.
Let's square the term where we have it in the denominator.
Squaring b/c we have a c^2 in the denominator, so multiply the cube of c/d...
Following this we see the following expression.
abc/def=a/b*b^2/c^2*c^3/d^3*/d^2/e^2*e/f
Now, we can just put the values.
abc/def=1/3*4*1/8*9*1/4=3/8.(A)
As we have one abc in the denominator and both the terms with b per the given data can be cancelled out.
Let's square the term where we have it in the denominator.
Squaring b/c we have a c^2 in the denominator, so multiply the cube of c/d...
Following this we see the following expression.
abc/def=a/b*b^2/c^2*c^3/d^3*/d^2/e^2*e/f
Now, we can just put the values.
abc/def=1/3*4*1/8*9*1/4=3/8.(A)
a/b=1/3
since we obtain an exact answer, we can suppose a=1 and b=3
so c must =1.5 since b/c=2
d= 3 using same reasoning
e=1
f=4
We have easy values to work with and have satisfied the ratio conditions.
abc= 1(3)(1.5)=4.5
def=3(1)(4)=12
we obtain 4.5/12
=9/24 and dividing numerator and denominator by 3 we obtain 3/8
since we obtain an exact answer, we can suppose a=1 and b=3
so c must =1.5 since b/c=2
d= 3 using same reasoning
e=1
f=4
We have easy values to work with and have satisfied the ratio conditions.
abc= 1(3)(1.5)=4.5
def=3(1)(4)=12
we obtain 4.5/12
=9/24 and dividing numerator and denominator by 3 we obtain 3/8
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Brent@GMATPrepNow
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Assign some values to the given variables.GMATinsight wrote:if a/b = 1/3, b/c=2, c/d = 1/2, d/e=3, and e/f=1/4 then find the value of abc/def?
A) 3/8
B) 27/8
C) 3/4
D) 27/4
E) 1/4
ans: A
Given: a/b = 1/3
Let a = 2 and b = 6
Given: b/c = 2
Since b = 6, it must be the case that c = 3
Given: c/d = 1/2
Since c = 3 , it must be the case that d = 6
Given: d/e=3
Since d = 6 , it must be the case that e = 2
Given: e/f = 1/4
Since e = 2 , it must be the case that f = 8
So, abc/def = (2)(6)(3)/(6)(2)(8)
= 36/96
= 3/8
Answer: A
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
